Now showing items 41-60 of 96

• #### On Particle Interaction Models ﻿

(2014-02-24)
This dissertation deals with three problems in Stochastic Analysis which broadly involve interactions, either between particles (Chapters 1 and 2), or between particles and the boundary of a C2 domain (Chapter 3). In Chapter ...
• #### On special Lagrangian equations ﻿

(2014-02-24)
In this paper we study the special Lagrangian equation and related equations. Special Lagrangian equation originates in the special Lagrangian geometry by Harvey-Lawson [HL1]. In subcritical phases, we construct singular ...
• #### Lam-Williams Markov chains on symmetric groups ﻿

(2014-02-24)
This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ...
• #### Combinatorial Laguerre Series ﻿

(2014-02-24)
We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials. We describe how such a series can be computed by ...
• #### Path algebras and monomial algebras of finite GK-dimension as noncommutative homogeneous coordinate rings ﻿

This thesis sets out to understand the categories QGr A where A is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: \begin{enumerate} \item What is the structure ...
• #### Grothendieck Duality on Diagrams of Schemes ﻿

The Du Bois complex and Du Bois singularities, which extend results of Hodge theory to singular complex varieties, can be defined in terms of a cubical hyperresolution. In this dissertation I further develop the language ...
• #### Heat Kernel Estimates for Markov Processes Associated with Time-Dependent Dirichlet Forms ﻿

In this paper, time-inhomogeneous stable-like processes are investigated. We establish the relation between the transition operators and time-dependent parabolic equations, as well as upper heat kernel estimates.
• #### Toward the compactification of the stack of Lie(G)-forms using perfect complexes ﻿

To establish geometric properties of an algebraic stack, one can find a compactification. This method has been successfully employed to find irreducible components for example of the moduli stack of curves [DM69], vector ...
• #### The Positive Semidefinite Rank of Matrices and Polytopes ﻿

The positive semidefinite (psd) rank of a nonnegative <italic>p</italic> × <italic>q</italic> matrix <italic>M</italic> is defined to be the smallest integer <italic>k</italic> such that there exist <italic>k</italic> × ...
• #### Sheaves on support varieties and varieties of elementary subalgebras ﻿

We present several results about two closely related types of objects: the projectivized scheme $\PG$ of one parameter subgroups of an infinitesimal group scheme $G$ and the variety $\bE(\fg)$ of maximal elementary subalgebras ...
• #### Convex Optimization over Probability Measures ﻿

The thesis studies convex optimization over the Banach space of regular Borel measures on a compact set. The focus is on problems where the variables are constrained to be probability measures. Applications include ...
• #### On numerics and inverse problems ﻿

In this thesis, two projects in inverse problems are described. The first concerns a simple mathematical model of synthetic aperture radar with undirected beam, modeled as a 2D circular Radon transform with centers restricted ...
• #### Spectral Theory of Z^d Substitutions ﻿

In this paper, we generalize and develop results of Queffelec allowing us to characterize the spectrum of an aperiodic substitution in Z^d by describing the Fourier coefficients of mutually singular measures of pure type ...
• #### Some Linear and Nonlinear Geometric Inverse Problems ﻿

Inverse problems is an area at the interface of several disciplines and has become a prominent research topic due to its potential applications. A wide range of these problems can be formulated under various geometric ...
• #### The C*-algebra of a finite T_0 topological space ﻿

We are concerned with the following motivating question: how can one extend the classical Gelfand-Naimark theorem to the simplest non-Hausdorff topological spaces? Our model space is a finite $T_0$ topological space, or ...
• #### Competing Brownian Particles ﻿

Consider a finite system of N Brownian particles on the real line. Rank them from bottom to top: the (currently) lowest particle has rank 1, the second lowest has rank 2, etc., up to the top particle, which has rank N. The ...
• #### Alternate Approaches to the Cup Product and Gerstenhaber Bracket on Hochschild Cohomology ﻿

The Hochschild cohomology $HH^\bullet(A)$ of an algebra $A$ is a derived invariant of the algebra which admits both a graded ring structure (called the cup product) and a compatible graded Lie algebra structure (called the ...
• #### Matrix free methods for large scale optimization ﻿

Sequential quadratic optimization (SQP) methods are widely used to solve large-scale nonlinear optimization problems. We build two matrix-free methods for approximately solving exact penalty subproblems that arise when ...
• #### The Zeros of Elliptic Curve L-functions: Analytic Algorithms with Explicit Time Complexity ﻿

Elliptic curves are central objects of study in modern-day algebraic number theory. The problem of how to determine the rank of a rational elliptic curve is a difficult one, and at the time of the writing of this thesis ...
• #### Finite-Difference Methods for Second-Order Wave Equations with Reduced Dispersion Errors ﻿

Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate ...